Develop an MD-CRT robustness framework that trades dynamic range for increased error tolerance

Develop a multidimensional robust Chinese remainder theorem (MD-CRT) framework that reduces the dynamic range to achieve a larger vector remainder error bound τ for integer-vector reconstruction with matrix moduli, analogous to the robustness–range trade-off known for the one-dimensional robust CRT, including precise conditions and algorithms for reconstruction in the multidimensional setting.

Background

The paper focuses on a multi-stage MD-CRT scheme that improves robustness without reducing dynamic range. In contrast, in the one-dimensional robust CRT literature there is an established approach that explicitly trades dynamic range for greater robustness (larger τ).

The authors note that extending this dynamic-range–robustness trade-off to MD-CRT is challenging due to the matrix nature of moduli and the differences between robustly determinable ranges and fundamental parallelepipeds in higher dimensions, and they state that pursuing this direction remains an open problem.

References

The first approach is to reduce the dynamic range in exchange for a larger vector remainder error bound \tau, as what was studied in for robust 1D-CRT. The second, which is the focus of this section, is to enhance robustness without reducing the dynamic range through a multi-stage reconstruction framework as what is studied for robust 1D-CRT in . The first approach remains an interesting open problem for future research.

— Robust Multidimensional Chinese Remainder Theorem (MD-CRT) with Non-Diagonal Moduli and Multi-Stage Framework  (2604.00995 - Guo et al., 1 Apr 2026) in Section 5, Multi-Stage Robust MD-CRT (opening paragraphs)